Determining the phase difference between two electromagnetic signals is a widely needed measurement applied in a very large number of applications. In many of these applications, the two electromagnetic signals are combined (or “mixed”) in an apparatus that generates at its outputs one or more electromagnetic signals with an intensity that carries information about the phase difference between the two input signals.
Prior to the development of waveguide optics, mixing two electromagnetic signals was often performed using partially silvered mirrors, pellicles, or prisms. Now it is possible to combine two electromagnetic signals in an optical device called a 2×2 coupler. Electromagnetic signals delivered to the two input waveguides will interact and form superpositions of these signals on each of two output waveguides. The interaction can be created using evanescent coupling, multimode mixing, or waveguide branching.
In an evanescently coupled 2×2 coupler, the two input waveguides are brought close enough to each other to allow a portion of the electromagnetic radiation from either waveguide to transfer to the other waveguide. The amount of field transferred depends on the proximity of the two waveguides and how long the two waveguides remain close enough to transfer field energy. The region in which the waveguides are close enough together to allow a substantial amount of electromagnetic energy transfer is called the interaction region. An important aspect of this process is that the transfer of field energy from one waveguide to another imparts a ninety degree phase lag to the transferred field. The output signal intensities on each waveguide are then simply the square of the sum of these two electric field components within the waveguide.
This can be expressed mathematically as follows. The two input electric fields can be defined asEa=Aeiωt Eb=Beiωt+Δ
A and B are the scalar magnitudes, ω is the field frequency, and
Δ is the phase difference between the two signals.
Ia and Ib are the corresponding input electromagnetic intensities on waveguides a and b respectively, and are just the above-defined electric fields multiplied by their complex conjugate:Ia=EaEa*Ib=EbEb*
If we define f as the fraction of one input's intensity that remains on that waveguide at the output of the coupler, then we can write the output electric fields as:E′a=√{square root over (f)}Aeiωt+√{square root over (1−f)}Bei(ωt+Δ−π/2) E′b=√{square root over (f)}Bei(ωt+Δ)+√{square root over (1−f)}Aei(ωt−π/2) 
The output intensities I′a and I′b are then just the output electric fields times their complex conjugates:I′a=[√{square root over (f)}Aeiωt+√{square root over (1−f)}Bei(ωt+Δ−π/2)][√{square root over (f)}Ae−iωt+√{square root over (1−f)}Be−i(ωt+Δ−π/2)]I′b=[√{square root over (f)}Bei(ωt+Δ)+√{square root over (1−f)}Aei(ωt−π/2)][√{square root over (f)}Be−i(ωt+Δ)+√{square root over (1−f)}Ae−i(ωt−π/2)]
These expressions for intensity expand, and simplify to:I′a=fA2+(1−f)B2+2A2B2√{square root over (f(1−f))}cos(Δ−π/2)I′b=fB2+(1−f)A2+2A2B2√{square root over (f(1−f))}cos(Δ+λ/2)
If the spacing between the waveguides, and the length of this interaction region of the coupler are chosen to split equal amounts of each input signal onto each of the two output waveguides, then f=½ and the coupler is referred to as a 50:50 coupler. In this case, the output signal intensities can be described as:I′a=½Ia+½Ib+√{square root over (IaIb)} cos(Δ−π/2)i′b=½Ia+½Ib+√{square root over (IaIb)} cos(Δαπ/2)
These output intensities are sinusoidal functions of the input phase difference Δ and they are one hundred eighty degrees out of phase with each other. The one hundred eighty degree phase shift between the output signal intensities is a consequence of the ninety degree phase shift imparted during an evanescent transition between two waveguides.
The coupler behavior is affected by multiple properties (e.g. spacing between waveguides, length, curvature, varying indices of refraction). It is customary to refer to couplers by either the amount of light they couple (e.g. 50:50, 33:33:33, 10:90, etc.), or to reference the interaction length used in theoretical electromagnetic modeling calculations. That length is often the length, Lc50, needed to couple fifty percent of the light in a 2×2 coupler. In this way, an important aspect of the coupler can be specified independently from the details of how the coupler is designed. In this application, we will use both conventions. When referring to a 2×2 coupler, the XX:YY convention will generally be used, where XX is the “through” power, and YY is the “crossover” power. Therefore, if electromagnetic radiation is delivered to one input of a 10:90 coupler, ten percent will pass through without changing waveguides and ninety percent will be transferred to the adjacent waveguide and sustain a ninety degree phase delay. When referring to 3×3 couplers, a different convention will generally be used, and we will specify coupler lengths (also referred to as interaction lengths) in arbitrary length units in which a coupler length of about seven hundred eighty five such units couples fifty percent of the light across a 2×2 coupler.
The one hundred eighty degree complementary relation between the two output signals results in some serious disadvantages when using a 2×2 coupler for measurement of an input phase difference. The sensitivity of the measurement is close to zero for both output signals at the same input phase difference and these regions of insensitivity repeat every one hundred eighty degrees. In addition, there is no property of the output signals that indicates whether the input phase is changing in a positive or negative sense. We only observe that the outputs are changing sinusoidally. This ambiguity is a serious problem in most phase measurement applications. For example, in a surface topology measurement where the surface height controls the phase of one of the input signals, it is important to know whether the surface is advancing towards, or receding from the detector.
Multi-port couplers can be designed to overcome these disadvantages. Prior systems have used a 3×3 coupler to produce three output signals for a phase measurement device with more uniform sensitivity. These systems can also determine the direction of input phase progress.
A 3×3 coupler can be made by twisting three fibers A, B, and C together and then heating and pulling them such that the three fibers fuse to form a composite optical fiber with a substantially triangular cross section. FIG. 1 shows the device in schematic form where the three-dimensional character of the coupler is represented by the intertwining of the three waveguides A, B and C. FIG. 2 schematically shows the idealized symmetry of the triangular cross section of the three fibers. In this arrangement, any one fiber is in equal contact with both of the other two fibers. As a consequence of this, light injected on fiber A couples to both fibers B and C, and then also mutually couples from B to C and from C to B. This extra mutual coupling produces an additional phase lag for the light in waveguides B and C with respect to the light in waveguide A. As a result, when the coupler interaction length is chosen to produce equal intensities in each of the three output waveguides, the light in waveguides B and C is one hundred twenty degrees out of phase with the light in waveguide A, not just ninety degrees as it was in the 2×2 coupler case. Under actual conditions the phase delay may be somewhat different than one hundred twenty degrees.
When equal intensity inputs are injected into any two waveguides, as suggested schematically in FIG. 3, a unique property of this waveguide arrangement is that it produces a one hundred twenty degree phase relation between the intensities of the three outputs A′, B′, and C′ as a function of the phase difference between the two input signals. This unique output phase relation is plotted as a function of input phase difference in FIG. 4.
The one hundred twenty degree output phase relation eliminates the phase direction ambiguities, and phase sensitivity loss problems that are caused by the one hundred eighty degree phase relation inherent in 2×2 couplers. With three phases, the direction of phase progress is indicated by the cyclic permutation of the phases progressing “forward” as A′, B′, and C′, or “backwards” as A′, C′, and B′. In addition, it can be seen that whenever one phase is near a maximum or minimum intensity, the other two phases have relatively steep slopes. Because of this, the three output intensities carry information about the input phase in such a way that the device has essentially uniform phase sensitivity throughout the entire domain of input phase differences.
To simplify the assembly, reduce costs, and improve aspects of system integration, it is desirable to integrate components such as these 3×3 couplers into a planar optical waveguide such as that depicted in FIG. 5. Note that the three-fold symmetry is lost and the mutual coupling between waveguides A and C is dramatically reduced. It becomes clear that the planar coupler of FIG. 5 cannot manifest the same properties as the three-dimensional 3×3 fused coupler.
FIG. 6 shows a schematic representation of the planar 3×3 coupler, and indicates signal being introduced into waveguide B. Each single mode waveguide is illustrated here as a single line. The two-dimensional nature of this coupler is suggested by the lack of intertwining of the waveguide lines. The evanescent interaction region is suggested by the curved gathering of the three lines. We will refer to such a planar 3×3 device as a 3×3 subunit from here onwards to facilitate the description of the current invention in later sections.
FIG. 7 is a plot of the computed intensities of output waveguides A′, B′, and C′ as a function of the interaction length of the coupler in an ideal 3×3 planar subunit. Subunits will be referred to as ideal when path length variations, A to C coupling, and other effects are not taken into consideration. Signal couples off of waveguide B equally into waveguides A and C, and at two particular lengths, the intensity in waveguides A and C equal the intensity in waveguide B.
Alternately, if signal is injected into waveguide A (or equivalently C) as suggested in FIG. 8, the ideal 3×3 planar subunit does not produce uniform splitting for any interaction length. FIG. 9 illustrates this point with a plot of the output intensities of the three waveguides as a function of interaction length.
For the reasons described in the preceding two paragraphs, when light is injected into any two inputs of this 3×3 planar subunit, the advantageous uniform peak output intensities and one hundred twenty degree phase relation between the outputs that were found in the three-dimensional 3×3 couplers cannot be achieved using this 3×3 planar subunit.
At least one attempt has been made to make 3×3 multiphase interference devices using a single planar 3×3 subunit. The multiphase operation of this device depended on the additional phase shift produced by the differential propagation speeds of the inner and outer waveguides.
In this work, a 3×3 planar subunit was designed to produce roughly a one hundred twenty (plus or minus ten) degree output intensity phase relation as a function of the input phase difference of two signals injected on waveguides A and C. A serious limitation of this device was the lack of reproducibility of the output phase relation. Several variables must be precisely controlled in order to make the device reproducible and therefore manufacturable. The inter-waveguide coupling strength, total path length, and differential propagation speed must be chosen so that the additional phase shift would result in the correct optimal output phase relation for the same nominal coupler length. Since these properties are complex functions of the subunit construction parameters and all of these parameters are subject to variations in the fabrication process, it would have been difficult to achieve all targets simultaneously. This is evidenced by the large spread in output intensity phase relation reported.
Another limitation that was also a consequence of the lack of the precise one hundred twenty degree phase relation was that the third available output, waveguide B, which was not utilized for this reason, would not have the same maximum and minimum amplitudes as the two outputs on waveguides A and C. Also, the output on waveguides A and C did not span the full intensity range from zero to one hundred percent; at best they achieved about eighty five percent contrast. Because of this, the sinusoidal signals carrying the input phase information was riding on a DC bias level that was subject to drift, changes in the input laser power, and changes in the target object reflectivity.
All of these factors seriously complicate the interpretation of the output intensities into a corresponding precise determination of the input phase difference free from offset drifts, nonlinearities, and changes in the amount of light reflected back into an interferometric device.
Finally, depending on the materials used to make the waveguide, and the practical limitations controlling the dimensions and spacing of the waveguides, it can be difficult to achieve the needed additional phase shift required for a 3×3-like behavior unless the coupler structure is made very long. This extended length not only makes it more difficult to hit desired design parameter tolerance targets during the fabrication of the coupler, but it also makes the finished coupler more susceptible to changes in performance caused by temperature changes and substrate stress after manufacture.
Despite the inability of a 3×3 planar subunit to manifest all the desirable properties of a three-dimensional 3×3 coupler, a somewhat viable form of 3×3 coupler can be made in planar geometries using non-evanescent coupling devices such as a multimode interference device. Even though this device is planar, it achieves mutual cross coupling between waveguides B and C by using reflection and interference effects as described below. This device consists of three single mode waveguides which enter fairly abruptly into a larger waveguide segment that is capable of supporting multiple transverse modes, as depicted in FIG. 10. At the opposite end of this larger segment, three single mode exit waveguides carry three signals away.
The three signals entering the multimode waveguide region propagate and reflect off of the walls of the multimode waveguide region in such a way that interference effects cause the majority of the light to be “focused” back into the three single mode exit waveguides. The width and length of the multimode region is chosen so that the effective phase shift from waveguide A to B′ is the same as from A to C′, due at least in part to the reflections from the walls. In this way, the same electromagnetic behavior produced in a three-dimensional 3×3 fused fiber coupler, as depicted in FIG. 1, is replicated in a planar waveguide device, as depicted in FIG. 10.
One disadvantage of the multimode planar 3×3 coupler as depicted in FIG. 10 is the opportunity for impedance mismatches to arise if the coupler is not perfectly designed and manufactured. Even then, changes in the wavelength of the light used in the coupler can cause it to respond off of its design target because the interference, on which the device relies to provide perfect coupling without back reflections, is by nature wavelength dependent. For some applications, this disadvantage may be acceptable. For others, it is desirable to ensure near zero back reflections with more independence from wavelength, design, and manufacturing variations.
Unlike multimode interference couplers, evanescent couplers such as the three-dimensional fused fiber coupler depicted in FIGS. 1 and 2 are very adiabatic in their transition from three single mode waveguides to one coupled-mode waveguide (in the tapered fused region) and back out into the three single mode waveguides again. In this way, impedance discontinuities which produce back reflections are essentially eliminated.
The arrangements discussed so far have involved outputs separated in phase by one hundred twenty degrees and ninety degrees. Generally, two outputs with phase separations of any value can be useful for phase measurement as long as their phase separation does not get close to one hundred eighty degrees or zero degrees. It is just desirable to have phase separations of 360/M degrees, where M is an integer, in order to simplify the mathematical calculations of the phase difference. It follows that couplers with five, six, or even more outputs may also prove useful in certain applications.
In some applications, fewer than all of the available outputs of such a multi-port coupler can provide a desirable utility. For example, only two of the four outputs, representing sin(Δ) and cos(Δ), in a 4×4 quadrature system might be sufficient for many applications. So some of the outputs may be terminated or otherwise not used. Likewise, since in most applications the desire is to determine the phase difference between two input signals, these multi-port couplers may also have one or more inputs which are terminated or otherwise unused. Despite these terminations, the device will have at least three inputs and three outputs where the outputs have an intensity phase relation that is non-complementary (i.e. different from one hundred eighty degrees out of phase). So, we may define n and m as the “externally-connected” number of inputs and outputs while we retain N and M as representing the “internal” number of inputs and outputs.
The problem that remains however is how to produce such desirable multi-port evanescent couplers in a planar geometry where it is topologically impossible to place certain pairs of waveguides together to maximize coupling. What is needed, therefore, is an apparatus that overcomes problems such as those described above, at least in part.